Analysis Of Two-dimensional Photonic Crystals Research Articles

Band structure analysis of two-dimensional photonic crystals using the wavelet-based boundary element method

By adopting the scaling functions of the B-spline wavelet on the interval (BSWI) as interpolation functions, a wavelet-based boundary element method (BEM) model is constructed to compute the band structures of two-dimensional photonic crystals (2D PCs), which are composed of square or triangular lattices with arbitrarily shaped inclusions. The boundary integral equations of both the matrix and inclusion are developed in a unit cell because of the structural periodicity. In order to make the curve boundary be compatible well, geometric boundaries are interpolated by employing second order BSWI scaling functions while arbitrary order scaling functions are used to approximate boundary variables. For any given angular frequency, an effective technique is provided to generate matrix values related to the boundary shape. Moreover, singular integral problem involved in the presented wavelet-based BEM is considered. Then, combining the Bloch theorem and the interface conditions, a linear eigenvalue equation related to the Bloch wave vector is obtained. Numerical examples are given to verify the performance of the wavelet-based BEM developed herein compared with the conventional BEM.

Frequential and temporal analysis of two-dimensional photonic crystals for absorption enhancement in organic solar cells

We propose a theoretical study of the role of a two-dimensional photonic crystal in an organic solar cell. In particular, we use some specific resonant modes of the photonic crystal, that are not guided modes, to favor light trapping in the absorbing medium. The increase of optical path in the active layer causes an increase of absorption at some particular frequencies. A frequential-temporal analysis has been made to highlight the correspondence between absorption enhancement and photonic crystal resonant modes, in a thin absorbing slab. In addition we present possible designs that would broaden the absorption spectrum of the bulk material. Finally, we study a complete organic bulk heterojunction solar cell made of a 50nm-thick active layer, and a patterned ITO electrode. In such device, the well known trade-off between carrier extraction and light absorption can appear as a constraint. Our challenge is to obtain a high absorption in an ultra thin active layer solar cell, by using a light trapping effect.

Split-step finite-difference time-domain method with perfectly matched layers for efficient analysis of two-dimensional photonic crystals with anisotropic media

This Letter presents a split-step (SS) finite-difference time-domain (FDTD) method for the efficient analysis of two-dimensional (2-D) photonic crystals (PhCs) with anisotropic media. The proposed SS FDTD method is formulated with perfectly matched layer boundary conditions and caters for inhomogeneous anisotropic media. Furthermore, the proposed method is derived using the efficient SS1 splitting formulas with simpler right-hand sides that are more efficient and easier to implement. A 2-D PhC cavity with anisotropic media is used as an example to validate the efficiency of the proposed method.

Approximate analysis of two-dimensional photonic crystals with rectangular geometry II H-polarization

An approximate analytical approach for calculating the dispersion relations of two-dimensional photonic crystals, which was earlier developed for E-polarization, is extended for H-polarization (which is usually problematic for analytical treatment, because of field discontinuities). Useful analytical formulas, for calculating the dispersion relations and the magnetic fields, are developed. We show that the presented approach and the derived expressions provide a good approximation for a wide range of photonic crystal parameters. The results are also compared with accurate numerical calculations to check the validity of the approximations. This approach provides not only a fast way for photonic crystal calculations, but it also can be useful for the investigation of various physical effects as well as for the design and analysis of new photonic crystal devices.

Reduction of the staircasing error in the single-domain pseudospectral frequency-domain method for analysis of photonic crystals

An improved Fourier pseudospectral frequency-domain (PSFD) method is proposed for the analysis of two-dimensional photonic crystals. Similar to the conventional Fourier PSFD, this method also uses trigonometric basis functions to expand various components of the pseudoperiodic electromagnetic field. However, to avoid the staircasing error for curved boundaries, a convolution technique is introduced in the spectral domain. This results in a matrix representation of the Helmholtz eigenvalue problem. The latter can be solved readily for the photonic band diagram of a photonic crystal. This method shows not only excellent accuracy but also fast convergence in analyzing different types of symmetrical and nonsymmetrical photonic crystals.

Approximate analysis of two-dimensional photonic crystals with rectangular geometry I E polarization

Using analytical techniques the dispersion relations for two-dimensional photonic crystals with rectangular geometry are analyzed. In this part of the work E polarization is presented. By comparing with accurate numerical calculations, we show that our analysis provides a good description of the physical properties for this type of photonic crystal. Besides the significantly shorter calculation time, the analytical treatment provides an important insight into the photonic bands' formation and their properties. The presented approach and derived analytical expressions can be useful for the investigation of photonic band structures as well as for the design of novel photonic crystal devices.

Equal-frequency surface analysis of two-dimensional photonic crystals

This paper presents an analytical treatment of equal-frequency surface analysis of a two-dimensional photonic crystal. We first define the equal-frequency surface in terms of plane waves, which can be numerically evaluated. Then one- and two-plane-wave approximations are proposed, which consequently lead to analytical expressions of the equal-frequency surface. The approach presented is well suited to two-dimensional photonic crystals of weak dielectric modulation. For photonic crystals with a large modulation, the approach can be used to gain a general idea of the shape of the bands.

Principal Component Analysis of Results Obtained from Finite-Difference Time-Domain Algorithms

Finite-Differences Time-Domain (FDTD) algorithms are well established tools of computational electromagnetism. Because of their practical implementation as computer codes, they are affected by many numerical artefact and noise. In order to obtain better results we propose using Principal Component Analysis (PCA) based on multivariate statistical techniques. The PCA has been successfully used for the analysis of noise and spatial temporal structure in a sequence of images. It allows a straightforward discrimination between the numerical noise and the actual electromagnetic variables, and the quantitative estimation of their respective contributions. Besides, The GDTD results can be filtered to clean the effect of the noise. In this contribution we will show how the method can be applied to several FDTD simulations: the propagation of a pulse in vacuum, the analysis of two-dimensional photonic crystals. In this last case, PCA has revealed hidden electromagnetic structures related to actual modes of the photonic crystal.

Compact finite-difference frequency-domain method for the analysis of two-dimensional photonic crystals

A finite-difference frequency-domain method based on the Yee's cell is utilized to analyze the band diagrams of two-dimensional photonic crystals with square or triangular lattice. The differential operator is replaced by the compact scheme and the index average scheme is introduced to deal with the curved dielectric interfaces in the unit cell. For the triangular lattice, the hexagonal unit cell is converted into a rectangular one for easier mesh generation. The band diagrams for both square and triangular lattices are obtained and the numerical convergence of computed eigen frequencies is examined and compared with other methods.